On the definition of power factor and apparent power in unbalancedpolyphase circuits with sinusoidal voltage and currents

Definition for the apparent power S and for the power factor PF in unbalanced polyphase circuits with sinusoidal waveforms are presented. It is proved that the definition S²=(V_a²+V _b²+V_c²) (I _a²+I_b²+I _c²) has a definite physical meaning, leading itself to a convenient resolution in positive, negative and zero sequence, nonactive and active power. It is suggested that the power factor be represented with the help of the ratio P⁺/ S, where P⁺ is the positive sequence active powers     

Investigation of harmonic currents and power factor on power rectifier circuits with nonequi-PWM and equi-PWM control (inductive load)

Lately, on the power rectifier circuit with semiconductor switching device, PWM control is generally employed for the purposes of reducing the harmonic currents on the dc side and improving the power factor of fundamental wave. In this case, the analysis of the current waveform becomes fairly complex. However, we express the PWM controlled voltage waveform by the step function, and can easily analyze the current waveform. We reported formerly some results of analysis about the waveform and harmonics of the current. In this paper, on the power rectifier circuit to which the nonequi-PWM and equi-PWM control are applied, we exactly calculate the harmonic currents on the dc and ac side, and the power factor by the use of the above analytical results. The characteristics of both control methods are compared on condition that each controlled factor of the load voltage is equal. These results are shown in the calculated charts. The following items can be seen from these charts on the power rectifier circuit: (1) The nonequi-PWM control can let the harmonic currents on the dc side decrease more than the equi-PWM control. But on the contrary, the harmonic currents on the ac side increase. Consequently, when the nonequi-PWM control is applied, the total power factor decreases by the increase of distortion factor of the current on the ac side. (2) The difference between the harmonic currents on the dc and ac side to both of the nonequi-PWM and equi-PWM control increases with the increase of controlled factor of the load voltage. © 1999 Scripta Technica, Electr Eng Jpn, 129(4): 117–125, 1999     

The Buchholz-Goodhue apparent power definition: the practicalapproach for nonsinusoidal and unbalanced systems

In unbalanced, nonlinear polyphase power systems, the apparent power can be measured using a definition given by F. Buchholz (1922) and explained by W.M. Goodhue (1933). This apparent power is based on a practical approach that allows the evaluation of power components that affect unbalance, line losses, current distortion and power factors     

Misinterpretations of some power properties of electric circuits

It might be expected that the meaning of the apparent power S, a quantity of innumerable everyday applications for almost a century, is well understood. It occurs, however, that this meaning is still a matter of discussion and some interpretations hard to accept are published. Also it is suggested in some papers published recently that only oscillations of the instantaneous power may cause an increase of the apparent power S, which is not true. Misinterpretations that refer to fundamental notions such as powers could be particularly harmful for electrical engineering and should be eliminated as much as possible. Therefore, this paper shows that the apparent power does not have the physical meaning suggested recently. Also it shows that load unbalance in three-phase power systems does not cause any oscillation of the instantaneous power. The conclusion that load unbalance causes oscillations of the instantaneous power is a consequence of a substantial misinterpretation of this quantity in three-phase power systems     

非正弦和三相不对称系统中功率的实用计算

针对目前非正弦周期电流电路和三相不对称电路中功率的定义和计算中的缺陷，本提供了一种新的功率定义和实用计算方法。同时介绍了衡量三相系统不平衡度和谐波污染的量化指标。     

非正弦和不对称负载情况下的功率流向和计费标准

电力系统谐波和不平衡负载增长迅速,影响了电度表的计量,导致了计量电费的不合理现象.若以有功功率的积分为电度量,将造成供电部门的电费损失,这是由于非线性和不平衡负载向系统倒送谐波和非正序功率影响计量以及这些功率在系统中流通增加线损所致.同时,不产生谐波的线性用户却受到谐波和不平衡电流的影响.该文表明,在单相系统中,以基波功率的积分代替全功率的积分作为计量标准,将会消除这两方面的不利影响.在三相系统中,以正序基波功率的积分作为计量标准,同样可以消除这两方面的不利影响.     

非正弦和不对称负载情况下的功率流向和计费标准

电力系统谐波和不平衡负载增长迅速,影响了电度表的计量,导致了计量电费的不合理现象。若以有功功率的积分为电度量,将造成供电部门的电费损失,这是由于非线性和不平衡负载向系统倒送谐波和非正序功率影响计量以及这些功率在系统中流通增加线损所致。同时,不产生谐波的线性用户却受到谐波和不平衡电流的影响。该文表明,在单相系统中,以基波功率的积分代替全功率的积分作为计量标准,将会消除这两方面的不利影响。在三相系统中,以正序基波功率的积分作为计量标准,同样可以消除这两方面的不利影响。     

IEEE-519-based real-time and optimal control of active filters under nonsinusoidal line voltages using neural networks

In this paper, a fast and simple neural network (NN)-based control system for shunt active power filters operating under distorted voltage conditions is developed. The proposed system is an enhanced version of the optimal and flexible control (OFC) strategy with very fast and simple structure. In the proposed system, the time-consuming and complex nonlinear optimization algorithm required by OFC is replaced by a simple 3-layer perceptron NN. The NN is trained off-line using some random data based on the IEEE-519 Standard, while it can be used for a very wide range of new voltage waveforms in practice. The proposed system has been developed after introducing a new version of the OFC strategy in a-b-c frame of reference. This system satisfies both theoretical and practical requirements. Several simulation results using MATLAB toolboxes under highly distorted and unbalanced voltages have been provided to validate the ability of the proposed control system.     

Calculation of currents and voltages in faulted high phase order systems

This paper presents a method for calculating phase and sequence voltage and currents throughout a power system of mixed phase order (i.e. the system is perceived to be divided into an arbitrary number of different phase order subsystems) subjected to an arbitrary fault type at an arbitrary bus in the system. The approach used involves sequence [Z] methods. An example application is provided.     

Parallel operation of three-phase power transformers with different short-circuit voltages

Parallel operation of three-phase power transformers with different short-circuit voltages has been studied using a lab bench. The circuit diagram of the bench and experimentally measured vector diagrams of the currents in primary and secondary windings of the transformers have been presented. It has been found that, when the difference of short-circuit voltages of parallel operating transformers is more than 10%, both an arithmetic difference of currents and a great phase shift of secondary-phase voltages occur. As a result, one of the transformers becomes overloaded, while the other is underloaded. It has experimentally been found that the load current is determined by the geometrical sum of currents of secondary windings in transformers. It has been shown that one of the studied transformers works in the conversion mode and its currents are shifted by 180° with respect to the phase, which is the main reason for failure of the normal operational conditions of parallel transformers.     

An efficient diagnostic technique for distribution systems based on under fault voltages and currents

Service continuity is one of the major aspects in the definition of the quality of the electrical energy, for this reason the research in the field of faults diagnostic for distribution systems is spreading ever more. Moreover the increasing interest around modern distribution systems automation for management purposes gives faults diagnostics more tools to detect outages precisely and in short times. In this paper, the applicability of an efficient fault location and characterization methodology within a centralized monitoring system is discussed. The methodology, appropriate for any kind of fault, is based on the use of the analytical model of the network lines and uses the fundamental components rms values taken from the transient measures of line currents and voltages at the MV/LV substations. The fault location and identification algorithm, proposed by the authors and suitably restated, has been implemented on a microprocessor-based device that can be installed at each MV/LV substation. The speed and precision of the algorithm have been tested against the errors deriving from the fundamental extraction within the prescribed fault clearing times and against the inherent precision of the electronic device used for computation. The tests have been carried out using Matlab Simulink for simulating the faulted system.     

Comments on active power flow and energy accounts in electricalsystems with nonsinusoidal waveforms and asymmetry

Pricing of electric energy is based on the value of the integral of the load active power P measured by energy meters. At such a pricing, the electric power utilities waste some revenue for the energy delivered to current harmonic generating customers and/or customers causing current asymmetry. This is because the load generated current harmonics and unbalanced currents cause an increase in the active power loss in the distribution system. At the same time, the customers that do not generate harmonics but are supplied with distorted and/or asymmetrical voltage are billed not only for the useful energy but also for the energy which may cause only harmful effects on their equipment. It is shown in the paper that these two disadvantages of the tariff in single-phase systems could be eliminated if the energy account based on the value of the integral of the active power of only fundamental harmonic, P_I, rather than on the integral of the whole active power P was used. These disadvantages could be eliminated in three-phase systems if the energy account is based on the integral of the active power of the positive sequence component of the fundamental harmonic     

非正弦波及不对称下三相功率因数的定义

尽管三相不对称下功率因数定义已有多种公式,但在非正弦波形又不对称下的功率因数定义依然存有争议。本文从单相非正弦波形下无功功率的时域分析定义出发,导出三相不对称时视在功率的公式,从而获得非正弦波形又不对称下三相功率因数的计算公式。     

An efficient technique for real-time control of system voltages and reactive power

This paper presents an efficient technique for the real-time control of reactive power dispatch. The proposed technique is based on a new voltage-reactive power model. This new model linearizes the load flow equations in Cartesian form with proper compensation to the second-order terms. The optimization process is non-iterative and thus is suitable for on-line applications. Different objective functions are incorporated in a global optimization technique and a multi-objective linear programming is formulated to solve this multiple decision-making problem. The non-dominance of the best compromise solution for the multiple objectives is assured by utilizing the operator-computer interactive capabilities of the multi-objective linear programming to reflect the urgency of the operating conditions and/or the predicted situations of the power system operation.     

Steep fronts at transient recovery voltages appearing with the interruption of inrush currents of transformers

High lightning overvoltages do not appear in underground substations connected to transmission cables. Consequently, it is very important to thoroughly investigate switching overvoltages and to achieve rational insulation coordination for apparatus installed in such underground substations. This paper discusses the occurrence of steep fronts at transient recovery voltages (TRV) appearing at circuit breakers when the inrush currents of transformers are interrupted. Caused by a steep front at the TRV, reignitions occur at circuit breakers, resulting in the generation of high overvoltages with high frequencies. The overvoltages are among the highest switching overvoltages appearing at the terminal of a transformer. The authors clarified the mechanism of the generation of steep fronts at TRV by means of EMTP analysis, as well as by carrying out tests in a high‐power laboratory. © 2001 Scripta Technica, Electr Eng Jpn, 135(1): 24–32, 2001     

Non-recursive methods for on-line estimation of voltages or currents and symmetrical components using Kalman filter theory

Using Kalman filter theory, new non-recursive algorithms for estimating the fundamental voltage and current waveforms from noise signals are developed and investigated. For non-harmonic random noise, these procedures have much better filter properties than Fourier algorithms, especially with increase in filter order and sampling frequency. The properties of the new methods in the time domain are also better than the Fourier ones. New algorithms for estimation of the symmetrical components are also developed and investigated. The use of the elaborated algorithms for protecting electric power systems has some advantages, owing to the convenient transient response time.     

Bearing currents and shaft voltages of an induction motor underhard- and soft-switching inverter excitation

Bearing currents and shaft voltages of an induction motor are measured under hard- and soft-switching inverter excitation. The objective is to investigate whether the soft-switching technologies can provide solutions for reducing the bearing currents and shaft voltages. Two of the prevailing soft-switching inverters, the resonant DC-link inverter and the quasi-resonant DC-link inverter, are tested. The results are compared with those obtained using the conventional hard-switching inverter. To ensure objective comparisons between the soft- and hard-switching inverters, all inverters were configured identically and drove the same induction motor under the same operating conditions when the test data were collected. An insightful explanation of the experimental results is also provided to help understand the mechanisms of bearing currents and shaft voltages produced in the inverter drives. Consistency between the bearing current theory and the experimental results has been demonstrated. Conclusions are then drawn regarding the effectiveness of the soft-switching technologies as a solution to the bearing current and shaft voltage problems     

Fast simulation technique for power electronic circuits with widelydifferent time constants

A technique for the fast simulation of transients is presented. The method combines the advantages of state-space averaging, decoupled simulation and envelope following. It is shown that simulation time can be reduced by a factor between 3 and 10⁵, depending on the example, without significant reduction of accuracy     

三电平逆变器缓冲电路内外电压不平衡分析及改进

针对三电平逆变器RCD缓冲电路在相邻开关状态之间转换时所发生的两种电压不平衡现象,进行了深入详细地分析,研究了产生电压不平衡的机理,并依据电路基本定律,推导了两种不平衡电压的计算公式。在此基础上,提出了一种简单的能使电压平衡的办法,并进行了仿真验证。结果表明性能良好。